There is no legal definition because even vegans don't fully agree on the definition, but there are branded certifications like "vegan society approved"
I would imagine that people with severe lacto-intolerance would need it most. Actual vegans - for ethical reasons - will find this incredibly horrifying.
Saying all that, though, I remember listening to a programme on the radio about how there was no definition of (cows) milk. At that time there were 50 or so different liquids containing all sorts of ingriedients that called themselves cows milk.
Veganism isn't an allergy and shouldn't be used as an allergen indicator. From the article I can't tell if the products are also missing suitable allergen labelling, the vegan alternatives I use always seem to indicate traces of animal products in the labelling.